{"paper":{"title":"On trees invariant under edge contraction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Olivier H\\'enard, Pascal Maillard","submitted_at":"2014-03-21T15:18:48Z","abstract_excerpt":"We study random trees which are invariant in law under the operation of contracting each edge independently with probability $p\\in(0,1)$. We show that all such trees can be constructed through Poissonian sampling from a certain class of random measured $\\R$-trees satisfying a natural scale invariance property. This has connections to exchangeable partially ordered sets, real-valued self-similar increasing processes and quasi-stationary distributions of Galton--Watson processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5491","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}